GPS drifts, and has to be calibrated several times a day. DGPS and WAAS make it more accurate from 100m to a few cm though.
True, Real Time Kinematic DGPS methods with a broadcast or cellular correction signal typically get you below 3 cm absolute horizontal.
On the other hand, fast static observations and post-processing typically yields sub centimeter (usually less than half a cm) results for absolute horizontal positions, even with broadcast ephemeris. You can usually tighten up positions if you wait for precise ephemeris calculations to be published for your time window.
As for any drift, it is taken care of automatically. The ground stations continuously sync the clocks on the space vehicles.